Find the y-coordinates of the points that are 10 units away from the point (-7, 6) that have an x-coordinate of 1.

For a given point (x₁, y₁) the set of all the points that are at a fixed distance R from the point form a circle, such that the equation of the circle is given by:

(x - x₁)^2 + (y - y₁)^2 = R^2

We will find that the two solutions are:

Here we want to find the y-coordinates of all the points that are 10 units away from the point (-7, 6) with an x-component of 1.

First, the circle will be:

(x + 7)^2 + (y - 6)^2 = 10^2

Now the x component must be equal to 1, so x = 1

(1 + 8)^2 + (y - 6)^2 = 100

81 + (y - 6)^2 = 100

(y - 6)^2 = 100 - 81 = 19

(y - 6)^2 = 19

(y - 6) = ±√19 = ±4.36

y = ±4.36 + 6

Then the two y-coordinates are:

y = 4.36 + 6 = 10.37

y = -4.36 + 6 = 1.64

So the two points are:

(1, 10.37) and (1, 1.64)

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